Pulling into the wooded Lexington neighborhood of modest, modernist 1950s houses, I hope I’ve got the right place. My confidence on this mid-September morning rises when I spot a Prius in the carport.

I knock twice before Jill Stein appears at the door in stocking feet. She clearly suspects I’m peddling something door-to-door, but she is unfailingly polite as she begs off through the glass. When I interrupt her to identify myself, she flashes a perplexed look. “I thought we were supposed to be meeting in Vermont?”

That’s right, I say, but there had been enough miscues with her overwhelmed press team that I decided to try to find her at home first.

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She tells me the previous night was the first in a month that she’d slept in her own bed. It’s been a hectic few weeks, from attracting an arrest warrant for spray painting a bulldozer during a pipeline protest in North Dakota to playing the conga drums with “Dancing in the Street” singer Martha Reeves at a rally in Detroit. During that stretch, she also sat down with the editorial board of The Washington Post, which later accused the Green Party presidential nominee of running a “fairy-tale candidacy” with ideas that are “poorly formed and wildly impractical.” Read the transcript of that interview and you can almost hear the snickering in the room. At one point, the editorial page editor asks her, “So $500 billion is all you need to get rid of oil, the internal combustion engine, and to give jobs to any American who wants a job?”

In many quarters, Stein and her outspoken running mate, Ajamu Baraka, have been dismissed as lefty loons. It’s true that some of her policy positions — cutting military spending in half and closing 700 foreign bases, getting rid of all fossil fuels within 14 years, guaranteeing a federal job to anyone who needs one — sound fanciful, and she occasionally stammers when asked to explain how she’d make them reality. It’s also true that her only successful runs for elective office have been for Lexington Town Meeting, a not-very-selective body whose membership tops 200. In the last decade and a half, she has kept running for higher and higher office, even as the percentage of the vote she attracts has basically kept shrinking. She put herself forward for Massachusetts governor in 2002, for state representative in 2004, for secretary of state in 2006, for governor again in 2010, for president in 2012, and again for president this year.

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Although she has developed a passionate Green following nationally, Stein admits that many people — even her own siblings — have asked her why she’s aiming for the highest office in the land. “Initially they were supportive,” she says of her two older sisters and younger brother. “Then they started to wonder why am I still doing this.”

Bill Weld is running a compressed campaign, a can’t-lose-even-as-he-loses shot in the arm. But for the 66-year-old Stein, running for president in two consecutive cycles has consumed the better part of several years of her life. And her rise in name recognition has been met with a deepening of the loopy-Lucy caricature.

If that’s partly because the numbers behind her ambitious proposals do not quite add up, a similar charge has been leveled against Hillary Clinton and her version of Bernie Sanders’s plan to provide free college for all. And against Donald Trump and his plan to build a wall to keep out Mexicans that they’ll somehow agree to pay for.

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Anyone who knows Stein only by the caricature would be surprised to learn that she may have the most impressive educational pedigree of anyone running for president. She went from top-five student at her competitive suburban Chicago high school to Phi Beta Kappa, magna cum laude graduate of Harvard, and then Harvard Medical School.

Don Treeger/Associated Press/File

Stein debating during the 2010 gubernatorial campaign, won by Deval Patrick (left).

I sit with Stein in her small kitchen as a cheerful aide fills Tupperware containers with lentil salad and organic berries to sustain the candidate on a campaign swing through northern New England. Hung on her older-model fridge is a peace decal and a clipped Marmaduke comic strip. The latter pays homage to Stein’s beloved Great Dane, Bandita, who died last year, the day she returned from her first trip of this presidential campaign.

Stein and her husband, transplant surgeon Richard Rohrer, moved with their two middle school-age sons from Cambridge to Lexington in 1995. Her boys are both grown now, both in their early 30s, both following their parents into medicine, one a resident in anesthesia at Tufts Medical Center, the other a student at UMass Medical School. Both, she says, are too busy to be involved in their mother’s campaign.

In the dark living room, where Stein’s conga drums sit next to an upright piano, there are copies of sailing magazines stacked on an end table. Her husband’s reduced schedule has allowed him to spend time on the boat he recently bought. “I still haven’t seen it,” Stein says. He’s not involved in her campaign, “except as a sort of sponsor and moral support. He’s not a political animal, as I wasn’t either.”

Until 1991, Stein had lived a don’t-rock-the-boat life, going from compliant, studious child of a lawyer father and homemaker mother to conventional mother and wife herself, albeit one with a career as an internist at Harvard Community Health Plan.

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Then, at the age of 41, she started getting punishing headaches. She went for an MRI, and the tech told her, “Hmm, we’re not seeing any blood flow on the left side of the brain.” She had a carotid artery dissection, which is a tear in the layers of the artery wall that diverts blood from getting to the brain. It’s the leading cause of strokes in the kind of young, healthy people who don’t usually have strokes.

Fortunately, she and her doctors caught the problem before there was neurological damage, and she recovered with medication. “It was like a big breaking point in my life,” she says. “I really thought long and hard about what do I want to do with my days now that I’ve seen my mortality right in front of my face.”

She spent more time writing and performing folk music, even contemplating a move to full-time musician. She hadn’t seriously considered that since her first year out of college, when she was a troubadour in Harvard Square. Ultimately, she settled on part-time doctor, part-time health-environmental researcher, and part-time environmental activist.

She spent years working to clean up dirty coal plants and shut down dirty incinerators. But it took a decade before her activism thrust her onto the public stage, when the Greens, a political asterisk in deep-blue Massachusetts, tapped her to run for governor. Hearing her tell it, she sounds like a volunteer who was the last one sitting in a school auditorium as a PTA meeting ran late and then somehow found herself nominated to be the group’s next president.

She ran with it. Fourteen years and a half-dozen campaigns later, that first race continues to occupy a favored position on her greatest-hits mix tape. She still talks often about winning an instant viewer poll after the first televised debate in that 2002 gubernatorial race against Olympic savior Mitt Romney and state treasurer Shannon O’Brien. By Election Day, though, she snared just 3.49 percent of the vote, though that was more than double the 1.43 percent she got when she ran again for governor in 2010.

Charles Krupa/Associated Press/File

Stein (far right) before a debate in the 2002 gubernatorial race.

Despite those and her other losses in Massachusetts, Stein used her doggedness as a grass-roots campaigner and relationship builder to expand her national profile in the Green Party to the point where she became its presidential nominee in 2012. Although she garnered just 0.36 percent of the popular vote in that race, her 469,627 tally was more than any female presidential nominee in US history. All that, plus her refusal to shy away from confronting Democrats and Republicans alike, helped her capture more than 80 percent of delegate votes at this year’s Green Party convention.

As soon as Stein steps into the student center of Vermont Law School in South Royalton, where the day’s first rally is taking place, the crowd of about 130 bathes her in adulation. Noted for its pioneering environmental law program, the school is fertile ground for the environmentally rooted Green Party. Campaign volunteers say they’ve been seeing a firehouse of new Green Mountain supporters ever since Bernie Sanders endorsed Clinton. They call them “third-degree Berns”: Sanders supporters so upset by his failed presidential bid that they jumped to Stein. (First-degree Berns pliantly shifted their votes to Clinton while second-degrees remain undecided.)

As two students take the stage to introduce Stein, she slips into a side room, next to the humming vending machines, to take a call. The students wrap up faster than she expected, because after they announce “Green Party nominee, Dr. Jill Stein!” there’s an awkward delay. It stretches so long that I find myself imagining Stein in peasant garb slipping over the border with the von Trapp family.

Eventually, Elizabeth Parker, Stein’s volunteer coordinator for the state, grabs the mic to kill time. (“How many people are from South Royalton or Bethel? Awesome. Burlington? Montpelier? Northeast Kingdom? Hey, bravo!”)

But as soon as Stein appears, all is forgiven, as the crowd of young law students and gray-haired progressives applaud and hoot their way through her talk.

During the question-and-answer period, a young redhead with glasses begins a question about corn subsidies but stops to apologize for her nerves. “I’m a little bit star-struck,” she gushes. “I adore you.”

So it goes for most of the long line of questioners. Whether they’re asking about Big Sugar, Big Media, or Big Oil, they all seem to come from a place of love. Stein remains soft-spoken even when she describes her industrial-strength rage at the corporate machine, describing herself as “a mother on fire.”

A couple of questioners tiptoe up to the line of eyebrow raising. One asks the inevitable “spoiler” question: Won’t Stein feel awful if the votes she collects drain enough support from Clinton to make Trump president, just as Ralph Nader (allegedly) sunk Al Gore in 2000? This question has become more pressing for her and the Johnson-Weld ticket, because while their poll numbers failed to qualify them for the debates, they have not shrunk much as the election nears, breaking the typical pattern for third-party candidates. Stein inveighs against the trap of the “lesser of two evils” argument. On climate change, she argues, the “all of the above” energy policy under President Obama “is arguably worse for the climate than ‘drill, baby, drill’ was under George W. Bush.”

A young bearded guy asks how Stein will fulfill her campaign promise to phase out the nation’s use of all fossil fuels by 2030 (meaning Stein’s eco-friendly Prius hybrid would become as unacceptable as a ’78 Impala). Improbably, her reply focuses on freeing up the talent of young Americans by erasing their college debt. I could almost hear a fresh round of snickering start to rise at the Washington Post.

With time running short before Stein has to leave for another event, Parker, her volunteer coordinator, breaks it to the crowd that Stein will not be able to do her usual routine of posing with supporters for individual selfies after the talk. “We’re just going to do a big group picture,” Parker says. Stein overrules her, politely, saying she’ll be extra brief to make time for all those selfies. She struggles to be succinct.

SUZANNE KREITER/globe staff

Jill Stein with supporters at a rally in Providence in September.

On the drive to her next campaign stop, at the University of New Hampshire, our discussion turns to Stein’s family. One of her siblings, she admits, is a diehard Democrat and sure to vote for Clinton. “Can you at least count on the votes of the other two?” I ask.

“I don’t put them on the spot,” she replies.

On the piano in her Lexington living room, I had seen sheet music labeled “for Mom,” with lyrics that dealt with how we all end as ashes. When she says she wrote the song for her mother, I ask what her parents made of their compliant daughter’s path, as it became increasingly radical, complete with multiple arrests for civil disobedience. They were proud of her, she says, though her mother would ask, “Why are you running in a little party? Why aren’t you running as a Democrat?”

Both of her parents died of Alzheimer’s disease. Despite the disease’s genetic component, she says that those twin storm clouds do not weigh heavily on her. Instead, it inspired her to review the research on neurodegeneration, which led her to argue that the odds of developing it can be greatly decreased with a good diet, exercise, and avoiding stress and exposure to toxic chemicals.

Her prognosis for the planet is less encouraging. “It could be curtains for us by 2050,” she says. Serving as a sort of perennial Green candidate for office is her way of being part of the solution. She keeps up her medical license (though not her insurance or prescribing privileges), but she doesn’t see herself ever returning to white-coat life. If her political crusade requires her to be away from home for months at a time and endure ridicule from the well-educated professional class of which she had long been a faithful member, so be it.

She says she’s not in this race for her own ego. That’s why she offered her slot on the ticket to Sanders if he’d go Green, though she was never able to get a response from him.

“I don’t need this,” she says.

It sounds like the only thing she’s said all day that she might not actually believe.